The generalized assignment problem with flexible jobs

Authors:
Chase Rainwater;Joseph Geunes;H. Edwin Romeijn
Affiliations:
Department of Industrial and Systems Engineering, University of Florida, P.O.Box 116595, Gainesville, FL 32611-6595, United States;Department of Industrial and Systems Engineering, University of Florida, P.O.Box 116595, Gainesville, FL 32611-6595, United States;Department of Industrial and Systems Engineering, University of Florida, P.O.Box 116595, Gainesville, FL 32611-6595, United States
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

The Generalized Assignment Problem (GAP) seeks an allocation of jobs to capacitated resources at minimum total assignment cost, assuming a job cannot be split among multiple resources. We consider a generalization of this broadly applicable problem in which each job must not only be assigned to a resource, but its resource consumption must also be determined within job-specific limits. In this profit-maximizing version of the GAP, a higher degree of resource consumption increases the revenue associated with a job. Our model permits a job's revenue per unit resource consumption to decrease as a function of total resource consumption, which allows modeling quantity discounts. The objective is then to determine job assignments and resource consumption levels that maximize total profit. We develop a class of heuristic solution methods, and demonstrate the asymptotic optimality of this class of heuristics in a probabilistic sense.